{"paper":{"title":"Optimal partition problems for the fractional laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonella Ritorto","submitted_at":"2017-03-16T14:32:29Z","abstract_excerpt":"In this work, we prove an existence result for an optimal partition problem of the form $$\\min \\{F_s(A_1,\\dots,A_m)\\colon A_i \\in \\mathcal{A}_s, \\, A_i\\cap A_j =\\emptyset \\mbox{ for } i\\neq j\\},$$ where $F_s$ is a cost functional with suitable assumptions of monotonicity and lowersemicontinuity, $\\mathcal{A}_s$ is the class of admissible domains and the condition $A_i\\cap A_j =\\emptyset$ is understood in the sense of the Gagliardo $s$-capacity, where $0<s<1$. Examples of this type of problem are related to the fractional eigenvalues. In addition, we prove some type of convergence of the $s$-mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05642","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}